Enhancing Line Density Plots with Outlier Control and Bin-based Illumination

TL;DR

This work tackles the breakdown of line continuity in density-based visualizations by introducing a bin-based outlierness metric and a structure-aware illumination pipeline. It decouples normals from density to build a dual normal map and applies per-bin, orientation-adaptive lighting confined to the luminance channel, enabling interactive emphasis on main trends or rare outliers with minimal color distortion. Key contributions include the bin-based similarity measure for ranking line trajectories, a dynamic structural-normal map composition, and an image-synthesis pipeline that supports user-driven balance between trend visibility and anomaly perception, scalable to thousands of lines. The approach is validated through ablation, color-distortion analyses, and real-world case studies, demonstrating improved detail over simple shading while preserving the original colormap and enabling real-time interaction for up to 10,000 lines.

Abstract

Density plots effectively summarize large numbers of points, which would otherwise lead to severe overplotting in, for example, a scatter plot. However, when applied to line-based datasets, such as trajectories or time series, density plots alone are insufficient, as they disrupt path continuity, obscuring smooth trends and rare anomalies. We propose a bin-based illumination model that decouples structure from density to enhance flow and reveal sparse outliers while preserving the original colormap. We introduce a bin-based outlierness metric to rank trajectories. Guided by this ranking, we construct a structural normal map and apply locally-adaptive lighting in the luminance channel to highlight chosen patterns -- from dominant trends to atypical paths -- with acceptable color distortion. Our interactive method enables analysts to prioritize main trends, focus on outliers, or strike a balance between the two. We demonstrate our method on several real-world datasets, showing it reveals details missed by simpler alternatives, achieves significantly lower CIEDE2000 color distortion than standard shading, and supports interactive updates for up to 10,000 lines.

Figures (11)

• Figure 1: Pipeline for enhanced, discretized line density plots: (a) Initial density plot; (b) Normal maps, including low- and high-frequency normal maps, composed by user defined parameters to construct a structure normal map for rendering; (c) Intensity map with user-controlled low- and high-frequency patterns computed from structure map via bin-based light direction optimization; (d) Illuminated density plot combining density and shading.
• Figure 2: The sensitivity of traditional Lambertian shading to a fixed global light direction. As the light comes from the northwest (left) versus the southwest (right), the set of highlighted line structures changes (see boxed section).
• Figure 3: Illustration of bin-based line similarity: (a) Construction of the distance field for a red line; (b) Discretized integral path over the red line’s field for a green line; (c) and (d) The discrete distance field of the green line, highlighting non-commutativity while limiting the diffusion range for efficiency.
• Figure 4: Ablation and comparative study on the vessel dataset frantzis2018hellenic (cf. \ref{['fig:teaser']}): (a) Without structure emphasis, the image appears flat and lacks detail; (b) A fixed global light introduces strong orientation bias (dashed box); (c) Direct RGB shading causes severe color distortion; (d) Scaled RGB shading still produces significant color distortion.
• Figure 5: Color difference ($\Delta E_{00}$) as a function of the illumination parameter $\phi$. Solid lines trace our method's distortion per dataset, while dashed lines show the higher, fixed distortion of the Lambertian baseline. The gray line marks our acceptable tolerance threshold of $\Delta E_{00} = 3.0$, based on printing industry benchmarks liu13discussion.